Maximal function characterizations for Hardy spaces on spaces of homogeneous type with finite measure and applications

The Anh Bui, Xuan Thinh Duong, Fu Ken Ly*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)

    Abstract

    We prove nontangential and radial maximal function characterizations for Hardy spaces associated to a non-negative self-adjoint operator satisfying Gaussian estimates on a space of homogeneous type with finite measure. This not only addresses an open point in the literature, but also gives a complete answer to the question posed by Coifman and Weiss in the case of finite measure. We then apply our results to give maximal function characterizations for Hardy spaces associated to second–order elliptic operators with Neumann and Dirichlet boundary conditions, Schrödinger operators with Dirichlet boundary conditions, and Fourier–Bessel operators.

    Original languageEnglish
    Article number108423
    Pages (from-to)1-55
    Number of pages55
    JournalJournal of Functional Analysis
    Volume278
    Issue number8
    DOIs
    Publication statusPublished - 1 May 2020

    Keywords

    • Hardy space
    • Maximal function characterization
    • Second order elliptic operator
    • Fourier–Bessel operator

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